{"status": "success", "data": {"description_md": "In rectangle $PQRS$, $PQ=8$ and $QR=6$. Points $A$ and $B$ lie on $\\overline{PQ}$, points $C$ and $D$ lie on $\\overline{QR}$, points $E$ and $F$ lie on $\\overline{RS}$, and points $G$ and $H$ lie on $\\overline{SP}$ so that $AP=BQ<4$ and the convex octagon $ABCDEFGH$ is equilateral. The length of a side of this octagon can be expressed in the form $k+m\\sqrt{n}$, where $k$, $m$, and $n$ are integers and $n$ is not divisible by the square of any prime. What is $k+m+n$?\n\n$\\textbf{(A) }1 \\qquad\n\\textbf{(B) }7 \\qquad\n\\textbf{(C) }21 \\qquad\n\\textbf{(D) }92 \\qquad\n\\textbf{(E) }106 \\qquad$", "description_html": "

In rectangle PQRS , PQ=8 and QR=6 . Points A and B lie on \\overline{PQ} , points C and D lie on \\overline{QR} , points E and F lie on \\overline{RS} , and points G and H lie on \\overline{SP} so that AP=BQ<4 and the convex octagon ABCDEFGH is equilateral. The length of a side of this octagon can be expressed in the form k+m\\sqrt{n} , where k , m , and n are integers and n is not divisible by the square of any prime. What is k+m+n ?

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\\textbf{(A) }1 \\qquad\n\\textbf{(B) }7 \\qquad\n\\textbf{(C) }21 \\qquad\n\\textbf{(D) }92 \\qquad\n\\textbf{(E) }106 \\qquad

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AMC 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10B_p18", "prev": "/problem/18_amc10B_p16"}}